Hello Owen, (what a neat moniker, BTW)
"My site seems to be running slow at times" is a very general and difficult to analyze problem. It doesn't seem likely (to me, at this point) that MySQL is at issue here. Can you try giving us some more information, like:
Is the site local to your test machine, or remote, and if so, about how many hops to the server?
What do your scripts look like, in general, and what do they do?
How heavily loaded is the server? Is it a shared server or a dedicated one? What do you know about its hardware, and what OS does it use? What is the server software? (What is the root password [just kidding!])....
How many hits is the site receiving daily?
As you say you "are using mysql_pconnect", you obviously have a clue that opening and closing and opening and closing a connection to the database can slow things down. But, there are a lot of other issues that you didn't address in your post (maybe you've already thought about all these...). If you're sure that is related to MySQL, I'd sure go over to the database part of these forums and ask those guys how you can speed things up....
🙂